That happened to us with the QE2 some years ago. I answered the questions honestly ie affirmative to the question as to whether anyone had been sick in the past 24 hours or whatever time period specified. My daughter did have a slight fever so we were denied boarding. Cunard sent us home in a car and as far as they were concerned, that was the end of the matter. They washed their hands off us.
We claimed on our insurance so we did not lose out on the cost of the cruise and I asked Cunard to refund me the cost of our journey to the port, which they did.
I thought Cunard would contact us to arrange an alternative holiday but nobody did. Afetr a few days, I called them to ask what they were going to do for us. Since it was the peak summer season, there was almost nothing left that was suitable. They offered us a couple of fly cruises on other Carnival ships (Princess I think) which were no good to us. We had booked a year earlier so the original cruise was at a good price. I had expected that they would offer us an alternative cruise at the same rates but nope, it was the going rate which was much higher.
I was most unimpressed with the way they dealt with us but maybe this is standard for the industry.